Why does refraction + volume scatter cause a much darker result?
Solution

Set Properties panel / Scene / Bounces / Volume value to at least one.

Explanation

Probably your volume bounces is set to zero because it is the default setting. That means only direct lighting on volumes are allowed, however caustics¹ are not. The same goes for the diffuse bounces value: If you set it to zero, caustics will not be present² and the perfectly transparent refractive object will cast shadow.

¹ Caustics is actually simply indirect lighting, but is handled specially due to its noisy nature.

² No recursive indirect sampling (also known as bounce, hence zero bounce) allowed.

Alternative Solution

You could also disable shadow casting on the refractive object and leave the volume bounces zero. The result will have less noise, but will lack proper caustical shadows. Or you could set up fake caustics like this one: https://urchn.org/post/fake-caustics-in-cycles